Consistency and Rate of Convergence for Deep ReLU Neural Networks

Abstract Deep ReLU neural networks have received a tremendous amount of attention nowadays due to their excellent performance in computer vision and natural language processing. However, our understanding of deep ReLU neural networks is still limited. In this article, we obtained convergence rates for deep ReLU neural networks based on VC dimension and an improved bound on the covering number. As a byproduct of these convergence rates, the growth rates in the width and depth of a deep ReLU neural network can be determined to achieve consistency. Various simulation studies were conducted for verification.